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中科院数学与系统科学研究院

数学研究所

 

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报告人Akhil Mathew(Harvard University / University of Chicago)

 Derived induction and restriction theory

  2017.08.13(星期日),15:30-16:30

  点:数学院南楼N913

  要:Let G be a finite group. Then it is a classical result of Quillen that the group cohomology of G can be recovered, up to nilpotence, from the cohomology of its elementary abelian subgroups. Using ideas from descent theory, we introduce a class of genuinely equivariant spectra that can be recovered in a strong homotopical sense from their restrictions to a given family of subgroups. We obtain large classes of examples of such equivariant spectra and show in particular show that complex-oriented theories have this property with respect to the family of abelian subgroups. As a result, we obtain (by decategorifying) analogs of the F-isomorphism theorem as well as analogs of Artin and Brauer induction for complex-oriented theories. This is joint work with Niko Naumann and Justin Noel.

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